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lfunc_lfunctions • Show schema
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{'Lhash': '831861390808175951463118958681', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.9017115386102166, -5.0259118137817556], 'a6': [0, 0], 'a7': [13.061385698571065, 22.6229836471786], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 38.233237683719935, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '648.433', 'coefficient_field': 'CDF', 'conductor': 648, 'conductor_radical': 6, 'conjugate': '1712611220275169255098451646686', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.9017115386102166, 5.0259118137817556], [-62.5, -108.25317547305482]], [[1.0, 0], [-13.061385698571065, -22.6229836471786], [-171.5, 297.04671349806245]], [[1.0, 0], [-18.6229836471786, -32.25595386543769], [-665.5, 1152.6798124370878]], [[1.0, 0], [-15.168656353084868, 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'10.14991330705265516200263691189592'], 'prelabel': '2-648-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1833031369746, 'root_angle': -0.38888888888888895, 'root_number': '0.3420201433256687330440996146822595807630833675141606285 - 0.9396926207859083840541092773247314699362081342644646331*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.19444444444444445', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65622292977134755030525856861', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.89998902285964885557617514139', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43361761236127947384021016209', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 38.233237683719935, 'bad_primes': [2, 3], 'central_character': '9.4', 'conductor': 648, 'conductor_radical': 6, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/648/4/i/u/433/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-648-9.4-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-648-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.1833031369746, 'root_angle': -0.19444444444444448, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65622292977134755030525856861', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '831861390808175951463118958681', 'Lhash_array': ['831861390808175951463118958681'], 'label': '2-648-9.4-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/648/4/i/u/433/3'}